I'll do my best to answer these, but keep in mind this is just my perspective.
1. There is quite a bit of research on the academic side, less so in industry, though there still is some. One useful idea that can come out of using BSM is understanding which options are relatively expensive relative to others--for example, comparing implied vols makes comparing options through time on similar parts of the delta surface much easier. That being said, of course it still isn't perfect--there may be large vol events in between expirations, and different firms have different ways to address that (for example, by modeling how much variance should be priced into that event and subtracting it from the farther expiration, etc.).
2. One way to think of modeling a vol surface/smile is a "chopped up" version of Black-Scholes--i.e., modeling the implied vols at each strike, but not using the same vol to price each option. That allows you to model the skew, kurtosis on both sides, etc.
3. Accuracy and speed is huge, of course. Analytic formulas allow firms to have a better idea of the risk they have on, i.e., gamma vs. theta, vega exposure, as well as risk measures that don't draw directly from BSM, such as the exposure a firm has to skew changing (getting steeper, or even flipping) in a certain expiration.
Let me know if any of that isn't clear.
